Evaluate the Function v(3/2)=4/3pir^3

$v (\frac{3}{2}) = \frac{4}{3} π r^{3}$

Replace the variable $r$ with $\frac{3}{2}$ in the expression.

$v (\frac{3}{2}) = \frac{4}{3} \cdot (π {(\frac{3}{2})}^{3})$

Simplify the result.

Simplify the expression.

Apply the product rule to $\frac{3}{2}$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot (π (\frac{3^{3}}{2^{3}}))$

Raise $3$ to the power of $3$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot (π (\frac{27}{2^{3}}))$

Raise $2$ to the power of $3$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot (π (\frac{27}{8}))$

Combine $π$ and $\frac{27}{8}$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot \frac{π \cdot 27}{8}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$v (\frac{3}{2}) = \frac{4}{3} \cdot \frac{π \cdot 27}{4 (2)}$

Cancel the common factor.

$v (\frac{3}{2}) = \frac{4}{3} \cdot \frac{π \cdot 27}{4 \cdot 2}$

Rewrite the expression.

$v (\frac{3}{2}) = \frac{1}{3} \cdot \frac{π \cdot 27}{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $π \cdot 27$ .

$v (\frac{3}{2}) = \frac{1}{3} \cdot \frac{3 (π \cdot 9)}{2}$

Cancel the common factor.

$v (\frac{3}{2}) = \frac{1}{3} \cdot \frac{3 (π \cdot 9)}{2}$

Rewrite the expression.

$v (\frac{3}{2}) = \frac{π \cdot 9}{2}$

Move $9$ to the left of $π$ .

$v (\frac{3}{2}) = \frac{9 π}{2}$

The final answer is $\frac{9 π}{2}$ .

$\frac{9 π}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π}{2}$

Decimal Form:

$14.13716694 \dots$